Bulletin of geography. Socio–economic series

W. Zhang, B. Derudder, J. Wang, F. Witlox / Bulletin of Geography. Socio-economic Series / 31 (2016): 145–160

151

If we hypothesize that in the course of a day the 

boarding and alighting passengers are equivalent in 

any of the transit cities, then can be formulated as

1

:

 v

ix 

= v

xi 

= v

i

/2 (4)

 v

jx 

= v

xj 

= v

j

/2 (5)

To evaluate the number of passengers boarding 

at city ‘i’ and alighting at city ‘j’ (i.e. v

ij 

in table 1), 

we first survey the probability of boarding in city 

‘i’ and alighting in city ‘j’ for all passengers. For 

any passenger in the passenger distribution ‘V’, we 

believe that boarding in city ‘i’ and alighting in city 

‘j’ are two mutual independent events. According to 

the rule of the probability of two mutual independent 

events happening together, the probability of 

boarding in city ‘i’ and alighting in city ‘j’ can be 

obtained by multiplying the probability of boarding 

in city ‘i’ by the probability of alighting in city ‘j’. 

As a corollary, we can approximate the number of 

passengers boarding at city ‘i’ and alighting at city 

‘j’ (v

i,j

) from multiplying the number of boarding 

passengers at city ‘i’ (v

ix

) by the number of alight-

ing passengers at city ‘j’ (v

xj

):

 v

ij 

= α × v

ix 

× v

xj

 (6)

where α is a dummy parameter describing the rela-

tion between v

ij

 and the product of v

ix

 and v

xj

.

Combining the different equations, v

ij

 can be ex-

pressed as the function of dwell times:

 v

ij 

= α × r

2 

× (t

i 

× t

j

) / 4 

(7)

However, for the cities of origin or destination, 

the number of boarding or alighting passengers 

(v

ox

 or v

xd

) is equal to the total passenger volumes 

(v). In these cases, the number of passengers of 

boarding in origin city ‘o’ and alighting in transit 

city ‘i’ (or boarding in transit city ‘i’ and alighting 

in destination city ‘d’) is given by:

 v

oi 

= α × r

2 

× (t

o 

× t

i

) / 2 

(8)

 v

id 

= α × r

2 

× (t

i 

× t

d

) / 2 

(9)

Similarly, the number of passengers of boarding 

in origin city ‘o’ and alighting in destination city ‘d’ 

is given by:

 v

od 

= α × r

2 

× (t

o 

× t

d

) (10)

Based on equations (7-10), the volume of in-

ter-city passengers can be obtained in the form of 

multiples of ‘α × r

2

’. In the next section, we oper-

ationalize this approach by means of a case study.

4.  Approximating the flows of high-speed 

railway (HSR) passengers 

within the Yangtze River Delta

4.1.  Case region, data 

and transformed network

High-speed railway (HSR) travel plays an important 

role in facilitating individual movements, thus en-

abling the formation of larger labor markets in re-

gions and fostering wholesale regional integration 

(Zheng, Kahn, 2013; Blum et al., 1997; Chen, 2012). 

Since the first HSR

2

 in China became operational 

in 2007, China’s HSR network has been growing 

rapidly. By the end of 2013, its length reached 

10463 km, constituting the longest HSR network in 

the world. The Yangtze River Delta region is one 

of the main mega-city regions with intensive HSR 

networks, where 22 major cities—54% of the entire 

41 cities within the YRD

3

 (i.e., Shanghai, Nanjing, 

Hangzhou, Suzhou (Jiangsu), Hefei, Changzhou, 

Wuxi, Zhenjiang, Bengbu, Chuzhou, Huainan, 

Lu’an, Quzhou, Suzhou (Anhui), Xuzhou, Jinhua, 

Ningbo, Huzhou, Shaoxing, Taizhou (Zhejiang), 

Wenzhou and Jiaxing)—are interconnected through 

HSR (fig. 1). Our empirical analysis focuses on the 

passenger flows of HSR among these 22 cities.

Data were gathered from the official website of the 

customer service center of China’s railway (www.12306.

cn). This website offers precise information on train 

operations, which includes prices, transit stations, 

and dwell times. To iron out the possible effects of 

operational fluctuations, we mined the information of 

all HSR trains transiting any city of the YRD region 

on a fixed day (February 24th, 2014). For every train, 

we recorded cities of origin and destination, transit 

cities and their dwell times. The end product that 

 - 10.1515/bog-2016-0010

Downloaded from De Gruyter Online at 09/23/2016 11:26:34AM

via Universiteit Antwerpen

---

W. Zhang, B. Derudder, J. Wang, F. Witlox  / Bulletin of Geography. Socio-economic Series / 31 (2016): 145–160

152

details the situation of transits (dwell times) is a city-

train matrix of 657 trains across the 22 cities. Apply-

ing our method, the transformed inter-city network 

is shown in fig. 2, in which edge thickness reflects the 

flow strength of city-pairs and node size reflects cit-

ies’ volumes of passenger flows.

Fig. 2. The transformed network of passenger flows within the Yangtze River Delta

Source: Own studies

The transformed network only connects cities 

along the HSR network; therefore, only 207 valid 

(nonzero) inter-city connections in terms of HSR 

passenger flows are presented in this network. The 

largest flow is between Shanghai and Nanjing, with 

344 HSR trains operating between them daily; the 

smallest flow is between Changzhou and Quzhou, 

where only two HSR trains operate on a daily basis. 

Parallelling the central corridor of the YRD urban 

agglomerations (Gu et al., 2007), we can observe the 

 - 10.1515/bog-2016-0010

Downloaded from De Gruyter Online at 09/23/2016 11:26:34AM

via Universiteit Antwerpen

---